Question

The formula m = 12,000 + 12,000(0.05)t 12t gives Keri's monthly loan payment when the annual interest rate is 5% and t is the length of the loan, in years. What are the asymptotes of the function? Explain what the asymptotes represent in context.

Answer 1

This is for the question: The formula m = 12,000 + 12,000rt /12t gives Keri's monthly loan payment, where r is the annual interest rate and t is the length of the loan, in years.

Explain why the formula is a rational function for a given value of r. What if you are given t?

It is of the form p(x)/q(x) where p(x) and q(x) are polynomials, and q(x) does not equal zero.

If r is given, it does not change the fact that there is still a variable in the denominator.

If t is given, there is no longer a variable in the denominator. The function is still rational, but the case of t being a constant, it is also linear.

Answer 2

The vertical asymptote is x 0.

The horizontal asymptote is y 50.

The vertical asymptote shows there is no monthly payment for a loan of 0 years.

The horizontal asymptote shows that as the length of time for which the loan is taken out increases, the monthly payment decreases. The monthly payment approaches, but never gets to $50 a month. This is because longer loans have greater simple interest up front.